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# If n and y are positive integers and 450y=n^3, which of the

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Manager
Joined: 21 Dec 2005
Posts: 103
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If n and y are positive integers and 450y=n^3, which of the [#permalink]  04 Apr 2006, 01:30
If n and y are positive integers and 450y=n^3, which of the following must be an integer?

I. y/3*2^2*5

II. y/3^2*2*5

III. y/3*2*5^2

Thanks
Manager
Joined: 20 Nov 2004
Posts: 108
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450y = n^3
2*3^2*5^2 y = n^3
So if both n and y are integers, we need to have a look
at what the least y could be so that 450 y = n^3.

The least possible y is 2^2*3*5, cause these are the
missing parts so that a third cube out of the term could
lead to an integer (--> n).

450 * 2^2*3*5 = (2*3*5)^3

So even in this case, y is divisible by 2^2*3*5.

Manager
Joined: 21 Dec 2005
Posts: 103
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Kudos [?]: 1 [0], given: 0

Good explanation ccax

Thanks
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